and phase response differs a lot from the original MZT phase response:

I've measured (as c/c++ function) this approximation method about 20 times faster than using std::exp function.

Idea used here is to use approximation ($e^x$ (exp(x)) using Taylor series (or other approximation methods) in this case) error to cancel the error in MZT/IIM methods ... when higher degree polynomial is used the error decreases and the resulting filter closes the original MZT/IIM responses. See the values for s, c and v, v2: https://www.desmos.com/calculator/s5wftcupmr

Someone, with better math skills than what I have, can easily improve this idea by finding better polynomial with suitable error to better cancel the error in MZT/IIM method.

Any thoughts on possible drawbacks in calculating one pole LP filter this way.

NOTE:
There are few well known methods available to improve the MZT/IIM type filters as like these:

$\begingroup$I get that IIM means Impulse Invariance Method. What does MZT mean? What are you trying to accomplish?$\endgroup$
– BenMar 27 '19 at 22:58

$\begingroup$it's the Matched Z-transform, @Ben . the most simple. just map the analog poles and zeros to the digital poles and zeros using $z=e^{sT}$.$\endgroup$
– robert bristow-johnsonMar 28 '19 at 0:02